A circuit is constructed with four resistors, one capacitor, one battery and a switch as shown. The
values for the resistors are: R1 = R2 = 54 Ω, R3= 83 Ω and R4 = 70 Ω. The capacitance is C = 78 μF and
the battery voltage is V = 24 V.
1) The switch has been open for a long time when at time t = 0, the switch is closed. What is
I1(0), the magnitude of the current through the resistor R1 just after the switch is closed?
I1(0)=24 V/(54+70)Ω = .19 A
2) What is I1(∞), the magnitude of the current that flows through the resistor R1 a very long time
after the switch has been closed?
I1=24 V/(54+54+83+70)Ω = .0919 A
3) What is Q(∞), the charge on the capacitor after the switch has been closed for a very long
time?
1. A current loop equation to find the voltage across the capacitor, Vc
First note I1=I4 at t->infinity
V-I1 R1-Vc-I4 R4=0 so Vc=V-I1 R1-I4 R4 = 24-4.96-70(.0919) = 12.607 V
2. Now use Q=VC
Q=VcC= 12.607 V(78 F)x 10-6=983.346 μC
4)
Consider the circuit above, with R5 = 60 Ω in series with the capacitor. Once again, the switch has
been open for a long time when at time t = 0, the switch is closed. What is I 1(0), the magnitude of the
current through the resistor R1 just after the switch is closed?
At t=0
V=IR1+IR523+IR4, where R235 is the equivalent resistance you get when you collapse R2, R3 and R5
into a single resistor. R23=R2+R3=137 Ω and 1/R235=1/R23+1/R5=(.007+.0167)1/ Ω so that R235=42.25
Ω
So I=V/(R1+R523+R4)=24 V/(42.25 Ω+54 Ω+70 Ω)=.144 A
4) Continuing with the new circuit, what is Q(∞), the charge on the capacitor after the switch has
been closed for a very long time?
Find I at a very long time. V=I(R1+R2+R3+R4), I=24/261=.09A
Find V across C: V=IR23=12.59V
Use Q=VC=(12.5V)(78uF)=982uC
A circuit is constructed with four resistors, one capacitor, one battery and a switch as shown. The
values for the resistors are: R1 = R2 = 57 Ω, R3= 81 Ω and R4 = 123 Ω. The capacitance is C = 38 μF and
the battery voltage is V = 12 V. The positive terminal of the battery is indicated with a + sign.
1) The switch has been open for a long time when at time t = 0, the switch is closed. What is
I4(0), the magnitude of the current through the resistor R4 just after the switch is closed?
Requiv=213.24 Ω
I4(0)=12 V/(Requiv)= .056 A
2) What is Q(∞), the charge on the capacitor after the switch has been closed for a very long
time?
Q=12 V 38 μF 81Ω/(57+81+123) Ω = 141 μC
3) After the switch has been closed for a very long time, it is then opened. What is Q(t open), the
charge on the capacitor at a time topen = 729 μs after the switch was opened?
Τ=(R2+R3)C=5244μs
Q(729 μs)=141 μC exp(-729 μs/T)=123 μs
4) What is IC,max(closed), the current that flows through the capacitor whose magnitude is
maximum during the time when the switch is closed? A positive value for the current is defined
to be in the direction of the arrow shown.
Ic=.033 A
5) What is IC,max(open), the current that flows through the capacitor whose magnitude is
maximum during the time when the switch is open? A positive value for the current is defined
to be in the direction of the arrow shown.
Ic=-.026 A